EA - Calculating how much small donors funge with money that will never be spent by Tristan Cook

Link to original articleWelcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Calculating how much small donors funge with money that will never be spent, published by Tristan Cook on January 16, 2023 on The Effective Altruism Forum.Epistemic status: Confident that the effect is real, though likely smaller than suggested by the toy-model.SummarySmall donors should discount the cost effectiveness of their donations to interventions above a large funder’s bar ifthey expect the large funder not to have spent all their capital by the time of AGI’s arrivaltheir donation to interventions above the large funder’s bar funges with the large funder.In this post I describe a toy model to calculate how much to discount due to this effect.I apply the model to a guess of Open Philanthropy’s spending on Global Health and Development (GHD) with Metaculus’ AGI timelines (25% by 2029, 50% by 2039). The model implies that small donors should consider interventions above OP's GHD bar, e.g. GiveWell's top charities, are only 55% as cost effective as the small donors first thought. For shorter AGI timelines (25% by 2027, 50% by 2030) this factor is around 35%.I use OP's GHD spending as an example because of their clarity around funding rate and bar for interventions. This discount factor would be larger if one funges with 'patient' philanthropic funds (such as The Patient Philanthropy Fund).This effect is a corollary of the result that most donor's AGI timelines (e.g. deferral to Metaculus) imply that the community spend at a greater rate. When a small donor funges with a large donor (and saves them spending themselves), the community's spending rate is effectively lowered (compared to when the small donor does not funge).This effect occurs when a small donor has shorter timelines than a large funder, or the large funder is not spending at a sufficiently high rate. In the latter case, small donors - by donating to interventions below the large funder's bar - are effectively correcting the community's implicit bar for funding.Toy modelSuppose you have the choice of donating to one of two interventions, A which gives a utils per $, or B, which gives b utils per $. Suppose further that the available interventions remain the same every year and that both have room for funding this year.A large funder F will ensure that A is fully funded this year, so if you donate $1 to A, then F, effectively, has $1 more to donate in the future. I suppose that F only ever donates to (opportunities as good as) A.I suppose that F's capital decreases by some constant amount f times their initial capital each year. This means that F will have no assets in 1/f years from now.Supposing AGI arrives t years from now, then F will have spent fraction min(ft,1) of their current capital on A.Accounting for this funging and assuming AGI arrives at time t, the cost effectiveness of your donation to A is then min(ft,1)a utils per $. Then if b>min(ft,1)a, marginal spending by small donors on B is more cost effective than on A.By considering distributions of AGI's arrival time t and the large funder's funding rate f we can get a distribution of this multiplier.Plugging in numbersI takeThe large funder F to be Open Philanthropy’s Global Health and Wellbeing spending on Global Health and Development and intervention A to be Givewell’s recommendations.I take 1/f, the expected time until OP's funds dedicated to GHD are depleted to be distributed Normal(20,20) bounded below by 5.I take AGI timelines to be an approximation those on Metaculus.These distributions on AGI timelines and 1/f give the following distribution of the funging multiplier (reproducible here).The ratio of cost effectiveness between GiveWell's recommendations and GiveDirectly, a/b, is approximately 7-8 and so small donors should give to interventions in the (5, 7)x GiveDirectly range.For donors with shorter timeli...